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Abstract

The angular diameter of Snell’s window as a function of maximum wave slope is calculated. For flat water the diameter is 97° and increases up to about 122° when the wave slope is about 16°. Steeper waves break and disrupt the smooth surface used in the analysis. Breaking waves produce a window almost 180° wide. The brightness of the dark area around Snell’s window is heavily influenced by turbidity and upwelling radiation, especially in shallow water.

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Like the rainbow, Snell’s window has certainly been observed for tens and perhaps hundreds of thousands of years. While the first mention of it we could find was in Minnaert [2], it has probably been discussed and named many times, the identity of the first person to do so or publish it being long lost.

M. Minnaert, The Nature of Light and Colour in the Open Air (G. Bell, 1940).

Water waves are not sinusoidal but in most cases are close enough to sinusoids that the analysis presented here is indicative of real-world waves. Indeed, regardless of the wave shape, it is the maximum wave steepness that determines the size of Snell’s window.

Other (7)

Like the rainbow, Snell’s window has certainly been observed for tens and perhaps hundreds of thousands of years. While the first mention of it we could find was in Minnaert [2], it has probably been discussed and named many times, the identity of the first person to do so or publish it being long lost.

M. Minnaert, The Nature of Light and Colour in the Open Air (G. Bell, 1940).

P. Laven, http://www.philiplaven.com/p20.html (retrieved May2014).

Water waves are not sinusoidal but in most cases are close enough to sinusoids that the analysis presented here is indicative of real-world waves. Indeed, regardless of the wave shape, it is the maximum wave steepness that determines the size of Snell’s window.

Fig. 6. Transmission of flat water producing Snell’s window (solid line) and reflectivity of the under surface of water producing Snell’s blanket. The angle from zenith is what an underwater observer would measure.

Fig. 7. For steeply inclined wave faces in breaking waves and turbulent, bubble-filled water, skylight can reach an underwater observer from a zenith angle of ∼90°. Thus skylight can be seen that originates from the entire upper celestial sphere (angular diameter ∼180°).